Long-term projections of the impacts of warming temperatures on Zika and dengue risk in four Brazilian cities using a temperature-dependent basic reproduction number

For vector-borne diseases the basic reproduction number R0, a measure of a disease’s epidemic potential, is highly temperature-dependent. Recent work characterizing these temperature dependencies has highlighted how climate change may impact geographic disease spread. We extend this prior work by examining how newly emerging diseases, like Zika, will be impacted by specific future climate change scenarios in four diverse regions of Brazil, a country that has been profoundly impacted by Zika. We estimated a R0(T), derived from a compartmental transmission model, characterizing Zika (and, for comparison, dengue) transmission potential as a function of temperature-dependent biological parameters specific to Aedes aegypti. We obtained historical temperature data for the five-year period 2015–2019 and projections for 2045–2049 by fitting cubic spline interpolations to data from simulated atmospheric data provided by the CMIP-6 project (specifically, generated by the GFDL-ESM4 model), which provides projections under four Shared Socioeconomic Pathways (SSP). These four SSP scenarios correspond to varying levels of climate change severity. We applied this approach to four Brazilian cities (Manaus, Recife, Rio de Janeiro, and São Paulo) that represent diverse climatic regions. Our model predicts that the R0(T) for Zika peaks at 2.7 around 30°C, while for dengue it peaks at 6.8 around 31°C. We find that the epidemic potential of Zika will increase beyond current levels in Brazil in all of the climate scenarios. For Manaus, we predict that the annual R0 range will increase from 2.1–2.5, to 2.3–2.7, for Recife we project an increase from 0.4–1.9 to 0.6–2.3, for Rio de Janeiro from 0–1.9 to 0–2.3, and for São Paulo from 0–0.3 to 0–0.7. As Zika immunity wanes and temperatures increase, there will be increasing epidemic potential and longer transmission seasons, especially in regions where transmission is currently marginal. Surveillance systems should be implemented and sustained for early detection.


Climate scenarios
In Fig A, we plot periodic splines fit to forecasted temperatures based on the 5-year historical data and each each climate change emission scenario for each city. The projected temperatures are similar among the different climate change scenarios.

Historical temperatures by year
In Fig B, we plot the best-fit periodic cubic spline approximations for the three Brazilian cities based on each individual year separately. The most notable yearly variation is the maximum temperature reached in Manaus.

Temperature dependent carrying capacity
The temperature dependent mosquito carrying capacity is defined as a function of other model parameters [1].
where T * =29 • C, κ B is the Boltzmann constant (8.617×10 -5 eV/K), and E A is the activation energy (set to 0.5) [1]. This parameter does not appear in the R 0 formula, but would be relevant to model simulation.

Temperature dependent model parameters
We plot the temperature dependent model parameters. In Fig C, we plot the temperature dependent biting rate, extrinsic incubation rate, and vector competence by pathogen. In Fig D, we merge two previous studies to arrive at an estimated temperature dependent mosquito lifetime. Finally, in Fig E, we revisit the temperature dependent extrinsic incubation rate for dengue, focusing on studies solely of dengue.   Temperature-dependent extrinsic incubation period data [2] were fit using a BriÃšre function parameterized by a Poisson maximum likelihood estimate. 6

Sensitivity analysis of R 0 (T )
First, we plot the R 0 (T ) curves holding each combination of the four temperature-dependent parameters constant at its mean value (giving 16 possible combinations). For each of the four parameters, we plot the 8 curves where it was held constant and the 8 where it follows the temperature-dependent distribution given in Table 1 (Fig F). Next, we assessed the width of the interval where R 0 (T ) is greater than half of its maximum value (full width at half maximum) for each curve and plot this for each parameter (Fig G). We do the same for the temperature at which the R 0 (T ) for each parameter combination reaches its peak value (Fig G).
In Fig F, we see that EIP (extrinsic incubation period) has the smallest impact on both the magnitude and the shape of R 0 (T (t)), while mosquito biting rate has a large impact on the magnitude. Fig G demonstrates that both EIP and lifespan have a small impact on the width of the R 0 (T (t)) distribution, while vector competence and biting rate have a lare impact. However, mosquito lifespan has the largest impact on which temperature the distribution reaches its peak R 0 (T (t)).   Figure G: Impact of fixing each temperature-dependent parameter on the full width at half maximum ((a) and (c)) and the temperature at peak R 0 (T (t))((b) and (d)). The graph for each vector trait has two box plots, with the lighter color corresponding to the trait being help constant at its mean value.

Sensitivity analysis of city-specific scenarios
Next, we show the sensitivity of the city-specific projections to the temperature-dependent parameters. Here, we remove the temperature-dependence of only one parameter at a time, corresponding to the parameter at the head of each column of Fig H (Zika) and Fig I (dengue). For each parameter, we show its impact on both the historical baseline and the highest SSP scenario (i.e., SSP 585).

Risk projections based on individual-year data for dengue
In Fig J, we give the risk projections based on individual year data for dengue (analogous to Fig 4 in the main text for Zika). As with Zika, dengue risk in Manaus may be slightly depressed in the hottest month of some years.

Basic reproduction number R 0 calculation
We use the next generation method to derive the basic reproduction number (R N GM 0 ) [4][5][6]. The infected subsystem from the equations for this model are as follows: We decompose the right-hand side of these equations as F − V, where F and V are as follows: From these, the Jacbobian matrices F of F and V of V can be obtained: Therefore, the next generation matrix is given by which has the following characteristic equation, 0 = λ 4 − λ 2 a(T ) · N m · π mh · σ m (T ) µ m (T ) · N h · (σ m (T ) + µ m (T )) a(T ) · π hm (T ) · σ h (σ h + µ h )(γ + µ h ) .